Flexural vibration resonator with high quality factor for the production of time standards, force sensors or gyrometers

Description

Domaine technique

[0001] The present description relates to a resonator with a vibrating portion which is formed in a wafer with parallel faces, as well as to a force sensor and a gyrometer which comprise such a resonator. Technique antérieure

[0002] Bending vibration resonators are widely used to produce time references, gyrometers and force sensors. The best known examples are the quartz crystal tuning fork to provide a time reference, as described for example in US 3,683,213, the double tuning fork to form a force sensor, as described for example in US 4,215,570, the double tuning fork to measure a rotational speed, as described for example also in US 3,683,213, or, still for measuring a rotational speed, the single tuning fork with a decoupling structure as described for example in US 6,414,416 B1.

[0003] In the case of quartz crystal piezoelectric resonators that vibrate in bending, the orientation of the resonator beam(s) is generally chosen along the Yc crystallographic axis, and the resonator planar structure is parallel to the Xc-Yc crystallographic plane. This allows on the one hand to optimally benefit from the piezoelectric coupling to excite and detect bending vibrations in the Xc-Yc and Yc-Zc planes, and on the other hand to benefit from the higher etching speed along the Zc axis to cut the structure using an acid-type wet etching process, generally with a mixture of ammonium fluoride (NH 4 F) and hydrofluoric acid (HF). Indeed, the piezoelectric tensor of trigonal class crystals offers an optimal coupling for the Syy deformation, i.e. along the beam axis, with an Exx electric field.For this, the bending vibration of the beam is excited by direct piezoelectric effect using electrodes which are located along the beam in order to generate the electric field Exx, and to detect the deformations Syy via electric charges which are generated by indirect piezoelectric effect on these same electrodes. Several alternative configurations are possible for the electrodes. For example, the electrodes can be arranged on both faces of the wafer in which the resonator is formed, as shown in [. Fig. 1a ] for vibration motions which are parallel to the Xc direction, or as shown in [ Fig. 1b ] for out-of-plane vibration motions that are parallel to the Zc direction. [ Fig. 1a] et [Fig. 1b ] further show for each electrode configuration represented the electric field component Exx which is useful for producing the bending of the beam. Such configurations with electrodes on the faces of the plate are simple to produce. But other electrode configurations are also possible, for example with the electrodes arranged on the sides of the beams which are perpendicular to the faces of the plate. Such other configurations are more effective for generating bending of the beams, but more difficult to produce, as described for example in US 4,524,619.

[0004] When these resonators are made by wet chemical etching of a wafer with parallel faces, etching facets that are due to the crystalline orientation of the etched planes generate asymmetries in the resonator pattern, which alter its subsequent operation. Indeed, in the case of class 32 trigonal symmetry crystals such as quartz, it is known that a Yc orientation beam that is chemically etched using a NH 4 F-HF mixture has a perfectly orthogonal flank in the Xc- direction and a dihedral on the orthogonal flank in the Xc+- direction. Then, due to the trigonal symmetry of quartz, this pattern is repeated every 120° (degree), as shown in [ Fig. 2a]. [Fig. 2b ] shows a typical result which is thus obtained for a quartz tuning fork whose plate faces are parallel to the Xc-Yc plane and the beams oriented longitudinally along the Yc axis. The facets fd on the sides of the tuning fork beams break the symmetry with respect to the plane P which is orthogonal to the plate faces, and the facets fo at the level of the beam embeddings break the symmetry with respect to the median plane M of the resonator.

[0005] These symmetry breaks cause poor dynamic balancing of the resonator, which generates vibration energy losses in the resonator attachment, and consequently degrades its quality factor and the stability of its vibration frequency. These degradations are detrimental to the use of the resonator to produce time bases or precision force sensors.

[0006] When such resonators are used to make vibrating gyrometers, the symmetry breaks of the resonator generally generate a parasitic mechanical coupling between two useful vibration modes of the gyrometer. This results in a measurement bias, i.e. the output signal of the gyrometer is no longer zero in the absence of rotation. The existence of such a non-zero measurement bias then greatly deteriorates the measurement accuracy of the gyrometer.

[0007] Compensation means are then implemented, generally in the form of masses which are added to the ends of the beams and which are adjusted by laser ablation, to reduce the imbalance and / or adjust the vibration frequency as described in US 3,683,213, or to reduce the quadrature coupling in the case of the vibrating gyrometers described in US 3,683,213.

[0008] Quadrature coupling for gyrometers arises from a mechanical coupling that connects two useful modes of gyrometer vibration: the so-called "pilot mode" which generally corresponds to the tuning fork vibration mode, and the out-of-plane vibration mode called "detector mode" which is excited by Coriolis acceleration from the pilot mode when the resonator is rotated around the longitudinal direction of the beams. In the presence of resonator symmetry breaking, mainly the breaking of symmetry about the midplane M (see [ Fig. 2b ]), a coupling stiffness appears between the pilot and detector modes, which generates a parasitic movement of the resonator in the detector mode in the absence of rotation. Such a defect strongly limits the performance of the gyrometer by introducing a measurement bias. However, implementing localized and individually adjusted laser ablations for each manufactured resonator, in order to correct such gyrometer symmetry defects is particularly expensive and often imperfect, so that the ultimate performance of the gyrometers remains limited.

[0009] Other clever ways to intrinsically reduce the quadrature coupling of quartz vibrating gyroscopes have been implemented, such as in FR 2 944 102 A1 in the name of the applicant. In FR 2 944 102 A1, the orientation of the vibrating beams is changed and a torsional vibration mode of the beams is used, which is coupled by Coriolis accelerations to a bending vibration mode. These changes allow for perfect symmetry of the vibrating structure while the resonator is still made using the low-cost chemical etching process of quartz. The quadrature coupling could be reduced in this way by 3 to 4 orders of magnitude, as reported by Guérard et al. in the article entitled "Quartz structures for Coriolis Vibrating Gyroscopes", DOI: 10.1109 / ISISS.2014.6782534, but to the detriment of the intrinsic thermal sensitivity of the gyrometer, which is very degraded because of the significant thermal dependence of the torsion mode, due to the intrinsic properties of quartz.

[0010] US 2006 / 0201248 A1 proposes an original structure of a quartz vibrating gyrometer, in which the sensitive axis is perpendicular to the plane of the structure, taking advantage of the trigonal symmetry of quartz and using three beams which are oriented along the crystallographic axes Yc. In this way, the gyrometer obtained benefits from a very good piezoelectric coupling between the pilot and detector modes. But such a vibrating structure is not symmetrical with respect to the plane which is orthogonal to that of the wafer when it is cut by chemical etching, and the vibration modes involved do not allow good dynamic balancing of the resonator to be obtained. The quality coefficients of the useful vibration modes are then degraded.

[0011] For force sensors, the double tuning fork structure described in US 4,215,570 represents an interesting compromise, in particular thanks to the very fine slot that separates the two beams intended to vibrate in phase opposition. This configuration ensures good coupling between the resonators while reducing the deformation of the beam embedding zones. In this way, a parasitic longitudinal movement that appears when the beams vibrate, and which causes energy dissipation, is reduced. This longitudinal movement is for example used in musical tuning forks, to transmit the vibrations of the beams to a resonant support through the foot of the tuning fork, in order to emit an audible sound that is very useful for tuning musical instruments. This example of exploitation of the longitudinal movement that is transmitted by the foot of the tuning fork clearly shows the energy leakage that occurs from the resonator to the outside, through its foot.On the other hand, the double tuning fork of US 4,215,570, when produced by chemical etching, also does not have symmetry with respect to a plane orthogonal to that of the resonator, because of the dihedral which is present on the orthogonal flank in the Xc+ direction. This geometric asymmetry also generates an asymmetry in the transmission of longitudinal forces in the two beams, making the frequency variations of the two beams which constitute the tuning fork unequal. This can then ruin the tuning fork effect, and greatly reduce the quality factor value which is effective when the resonator is subjected to an axial tensile force to be measured. Alternatives to the double tuning fork have been proposed for producing force sensors, such as that described in FR 2 574 209 A1 in the name of the applicant.FR 2 574 209 A1 proposes to combine a simple single beam resonator intended to vibrate in bending with systems for decoupling the vibrations of this beam from the support, via inertial masses which are arranged at the ends of the beam. This resonator has two advantages: on the one hand, a single blade instead of two for the tuning fork makes it possible to double the scale factor of the resonator, i.e. the frequency variation as a function of the axial tensile force to be measured, and on the other hand, the decoupling principle is very tolerant of alignment errors which may exist. But such a resonator remains bulky, which can limit its use in miniature devices such as accelerometers based on a resonator used as a sensitive element, and on the frequency variation which is associated with the force generated by a test mass via the acceleration to be measured.Another original alternative was proposed in FR 2 739 190 A1 also in the name of the applicant, by integrating a simple flexural resonator into a monolithic accelerometer structure and by providing a system for decoupling vibrations from the outside at the level of the monolithic accelerometer structure. An optimization of the simple resonator in flexural vibration was also proposed in FR 2 805 344 A1 also in the name of the applicant, by improving the value of the figure of merit F x Q / Sf, where F is the frequency of the resonator, Q is the quality factor of the resonance, and Sf is the scale factor expressed in Hertz by m / s 2< . This improvement is obtained by using a beam with a non-constant section which provides a gain of a factor of 1.2 on the figure of merit F x Q / Sf, representative of the stability of the accelerometer bias, i.e. the stability of the resonator frequency in the absence of acceleration.However, these simple resonators do not meet the applications of variable frequency force sensors which require the resonator to be intrinsically decoupled and insensitive to its fixing conditions to allow easy and reliable measurement of the force. From there, one aspect of the present invention is to propose a new force sensor which meets these intrinsic decoupling requirements, but no longer based on the modification of stiffness of the beam vibrating in bending, as produced by the axial force acting as a restoring torque and thus modifying the resonant frequency, but by modifying the bending inertia which is generated by the displacement produced by the force applied to the resonator. This principle of force sensor based on a modification of bending inertia has already been proposed, for example in the article "New resonant accelerometer based on rigidity change", Y. Omura, Y. Nonomura, O.Tabata, TRANSDUCERS 97, 1997, Internationnal Conf. Solid-State Sensors and Actuators, Chicago, but based on a non-decoupled resonator, which cannot satisfy demanding applications where a resonator with a high quality factor is required for measurement resolution and accuracy.

[0012] It is important to remember at this point that wet chemical etching to produce crystalline vibrating devices is an inexpensive process and particularly suitable for the mass production of micro-devices, while preserving the intrinsic quality coefficients of the crystal. Indeed, chemical etching, being based on a local chemical reaction, allows the crystal to be dissolved atom by atom without altering or degrading the crystal lattice of the material. This is not the case for etchings based on local abrasion, such as ultrasonic machining, which uses abrasive grains excited by ultrasonic waves generated between a probe (sonotrode) and the surface to be etched, or based on ion bombardment, which uses the kinetic energy of ions.These last two techniques alter the crystal lattice at the periphery of the engraving, over characteristic distances of a few tens of nanometers to a few micrometers for the most energetic engravings, which reduces the intrinsic quality coefficient of the resonators, especially since miniaturization of the device is sought. Problème technique

[0013] From this situation, an object of the present invention is to provide a new resonator which is improved with respect to at least some of the disadvantages of the previous resonators, as recalled above.

[0014] In particular, an object of the invention is to provide a resonator for which the vibration energy losses to the outside are reduced, in order to provide a quality factor value which is increased.

[0015] An additional aim of the invention is to reduce symmetry defects which may affect the shape of the resonator, originating from differences in etching speed which exist between different crystalline orientations of a material used to constitute the resonator. Résumé de l'invention

[0016] To achieve at least one of these aims or another, a first aspect of the invention provides a resonator which comprises: a portion of a plate with two opposite faces which are flat and parallel, the plate portion being intended to vibrate by bending during use of the resonator, and called the vibrating portion; and a support part, which is external to the vibrating portion and connected to it by an intermediate segment of the plate, called the foot, this foot being continuous in material with the vibrating portion and forming a rigid connection between the support part and the vibrating portion. In this resonator of the invention, the vibrating portion has a first plane of symmetry, called the median plane, which is parallel to the two faces of the plate and equidistant from these two faces, and a second plane of symmetry, called the plane of symmetry orthogonal to the plate, which is perpendicular to the median plane and passes longitudinally through the connection formed by the foot between the support part and the vibrating portion. The intersection between the median plane and the plane of symmetry orthogonal to the plate constitutes a median axis of the vibrating portion. The vibrating portion comprises two extensions which are each intended to vibrate by flexion, these two extensions extending from the foot symmetrically on each side of the plane of symmetry orthogonal to the plate.

[0017] According to features of the invention, each extension is provided with a longitudinal slot which crosses the vibrating portion perpendicularly to the median plane, from the plane of symmetry orthogonal to the plate towards a distal end of this extension, but without reaching this distal end, so that each extension is formed by a meander. The respective slots of the two extensions are symmetrical with respect to the plane of symmetry orthogonal to the plate, and meet at this plane of symmetry orthogonal to the plate.Thus, the vibrating portion comprises two primary segments which each connect the foot to the distal end of one of the extensions, and two secondary segments which are connected to each other at the level of the plane of symmetry orthogonal to the plate by respective proximal ends of these secondary segments, and which each extend to the distal end of one of the extensions to be connected to one of the primary segments at this distal end.

[0018] By virtue of such a configuration of the vibrating portion, and for a vibration mode of the vibrating portion which only involves displacements parallel to the median plane, and which is symmetrical with respect to the plane of symmetry orthogonal to the plate, the two primary segments have instantaneous velocity components, parallel to the median axis, which have a direction opposite at each instant during the vibration, to that of the instantaneous velocity components of the secondary segments, also parallel to the median axis. These opposite velocity orientations allow the momentum components associated with them to at least partially compensate each other, so that displacements which are transmitted to the foot by the vibrating portion are reduced. As a result, the resonator has vibration energy losses which are low, so that its quality factor can be high.

[0019] Advantageously, the vibrating portion may have a mass distribution such that the vibration mode which only involves displacements parallel to the median plane and which is symmetrical with respect to the plane of symmetry orthogonal to the plate, does not cause displacement of the foot parallel to the median axis. In other words, the compensation of the momentum components of the vibrating portion, which are parallel to the median axis of the resonator, may be exact or quasi-exact. In this case, the vibration energy losses through the foot of the resonator are zero or quasi-zero, and the quality factor may be very high.

[0020] In preferred embodiments of the invention, the wafer material may be monocrystalline of trigonal class and piezoelectric. In this case, the median axis of the vibrating portion is parallel to an Xc axis of the material, and the two primary segments as well as the two secondary segments of the vibrating portion are parallel to Yc axes of the material. In other words, one of the two extensions of the vibrating portion may be parallel to the Yc+ crystallographic axis and the other parallel to the Yc- crystallographic axis. For such embodiments, the two extensions of the vibrating portion may form an angle between them which is equal to 60°.In particular, the plate can be made of α-quartz crystal (α-SiO 2 ) or any other crystal of the trigonal system of symmetry class 32, such as gallium orthophosphate (GaPO 4 ), germanium oxide (GeO 2 ), gallium arsenate (GaAsO 4 ), or even crystals of the LGX family: langasite (LGS or La 3 Ga 5 Si0 14 ), langatate (LGT or La 3 Ga 5 ,5TaO,5O 14 ) or langanite (LGN or La 3 Ga 5 ,5NbO,5O 14 ).

[0021] Alternatively, the two extensions of the vibrating portion can form an angle between them which is equal to 180°.

[0022] When the wafer material is monocrystalline of trigonal and piezoelectric class, the resonator of the invention may further comprise: excitation means, adapted to generate deformations by bending of the vibrating portion, these excitation means comprising a first and a second electrode which are electrically insulated from each other, the first electrode comprising, on each face of the plate and for each primary or secondary segment, a strip of electrically conductive material which is arranged longitudinally on this segment, centrally in a width of the segment, and the second electrode comprising, also on each face of the plate and for each primary or secondary segment, two strips on this segment which are arranged on two opposite sides of the strip of the first electrode;and detection means, adapted to measure an amplitude of the bending deformations of the vibrating part which are generated by the excitation means during use of the resonator, these detection means comprising a circuit for detecting an electric current which appears in the first and second electrodes. ;

[0023] Generally for the invention, each extension of the vibrating portion may comprise, at its distal end and parallel to the median plane, a widening relative to the external longitudinal edges of the primary and secondary segments of this extension. Such widenings provide an additional degree of freedom for compensating for the momentum components of the vibrating portion which are parallel to the median axis. Thus, the design of a resonator according to the invention, and which has a high quality factor, is facilitated.

[0024] Also generally for the invention, the resonator may further comprise an additional portion of the plate, in the form of a segment and called a peduncle, which extends from the proximal ends of the secondary segments connected to each other, parallel to the median axis and in a direction opposite to the foot. This peduncle may also participate in obtaining the compensation of the components of quantity of movement of the vibrating portion which are parallel to the median axis.

[0025] Possibly, the resonator may comprise two vibrating portions which are formed in the same plate, and provided with respective peduncles. The two vibrating portions may then be connected to each other by their peduncles, being oriented oppositely to each other so that the respective median axes of the two vibrating portions are superimposed.

[0026] Alternatively, the resonator may further comprise two vibrating portions which are formed in the same plate, being connected to each other by the respective feet of these two vibrating portions, and oriented oppositely to each other so that the respective median axes of the two vibrating portions are still superimposed.

[0027] A second aspect of the invention provides a force sensor, which comprises a resonator according to the invention, with two vibrating portions connected to each other by their respective peduncles. Such a sensor is adapted to measure a tensile force which is applied between the respective feet of the two vibrating portions, and which is parallel to the median axes of the two vibrating portions.

[0028] Finally, a third aspect of the invention relates to a gyrometer which comprises at least one resonator according to the first aspect of the invention. The operation of such a gyrometer uses the coupling which is produced by the Coriolis accelerations between the vibration mode with displacements which are parallel to the median plane and a vibration mode for which the displacements are perpendicular to this median plane.

[0029] Preferably, the gyrometer may comprise a resonator with two vibrating portions which are connected to each other by their respective feet while being oriented in opposite directions. For such a configuration of the gyrometer, two distinct uses are possible, each with a single sensitive axis of rotation, depending on the pilot mode which is chosen. According to a first possible choice for the pilot mode, the two vibrating portions vibrate in phase opposition in this pilot mode. The Coriolis accelerations which are generated by a rotation of axis parallel to the common median axis of the two vibrating portions then excite an out-of-plane vibration mode which is dynamically balanced.According to another choice which is also possible, the two vibrating portions vibrate this time in phase in the pilot mode, and the Coriolis accelerations which are generated by a rotation around an axis which is perpendicular to the common median axis of the two vibrating portions and which is parallel to the median plane, excite another out-of-plane vibration mode which is also dynamically balanced. In a preferred embodiment of such a gyrometer with two vibrating portions which are connected by their respective feet while being oriented opposite to each other, the plate can be made of quartz crystal and each of the two vibrating portions has its extensions at 60° to each other and parallel to crystallographic axes Yc. Such a configuration makes it possible to obtain an optimal piezoelectric coupling for the vibration modes to be excited or detected, as well as a symmetrical embodiment of the resonator when it is manufactured by chemical etching. Brève description des figures

[0030] The characteristics and advantages of the present invention will appear more clearly in the detailed description below of non-limiting exemplary embodiments, with reference to the appended figures among which: [ Fig. 1a ], already commented, is a reminder of a first possible configuration of electrodes, suitable for piezoelectric coupling which can be used for the excitation and detection of bending vibrations of a beam in the plane, in the case of a beam material which is piezoelectric and belongs to the trigonal system and symmetry class 32, such as α quartz; [ Fig. 1b ], already commented, corresponds to [ Fig. 1a ] for a second possible electrode configuration that can be used for excitation and detection of out-of-plane vibrations; [ Fig. 2a ], already commented, is a reminder of trigonal symmetry; [ Fig. 2b ], already commented on, shows a tuning fork-shaped resonator as known from the prior art and obtained by chemical etching of a quartz crystal, using a mixture of ammonium fluoride and hydrofluoric acid, with the resulting symmetry breaks when the two beams of the tuning fork are parallel to the Y axis; [ Fig. 3a ] shows the quantities of movement which are involved for a tuning fork with parallel beams as known from the prior art; [ Fig. 3b ] corresponds to [ Fig. 3a ] for a tuning fork with non-parallel beams; [ Fig. 3c ] corresponds to [ Fig. 3b ] for a double tuning fork with non-parallel branches, making it possible to globally compensate for quantities of movement which are not balanced within each tuning fork; [ Fig. 4a ] is a plan view of a first resonator made of trigonal piezoelectric material, which is in accordance with the invention; [ Fig. 4b ] corresponds to [ Fig. 4a ] to show deformations of the useful vibration mode of the first resonator, and the associated momentum quantities; [ Fig. 4c ] corresponds to [ Fig. 4a ] to show electrodes thereof for exciting and detecting the vibration of the useful mode, in the case of a trigonal piezoelectric crystal of symmetry class 32, such as quartz, which constitutes the resonator; [ Fig. 4d ] is a sectional view of the first resonator, corresponding to [ Fig. 4c ] ; [ Fig. 5a ] corresponds to [ Fig. 4a ] when two possible improvements of the invention are used; [ Fig. 5b ] corresponds to [ Fig. 5a ] to show deformations of the useful vibration mode; [ Fig. 6a ] is a plan view of a second resonator made of piezoelectric material, which is also in accordance with the invention; [ Fig. 6b ] corresponds to [ Fig. 6a ] to show deformations of the useful vibration mode of the second resonator; [ Fig. 6c ] corresponds to [ Fig. 6a ], when a possible improvement of the invention is used; [ Fig. 6d ] corresponds to [ Fig. 6b ] for the resonator of [ Fig. 6c ] ; [ Fig. 7a ] is a perspective view of a first gyrometer which is in accordance with the invention, and shows deformations which are associated with a pilot mode of this first gyrometer; [ Fig. 7b ] corresponds to [ Fig. 7a ] but showing deformations that are generated from the pilot mode of [ Fig. 7a ] by a rotation around a first axis, ; [ Fig. 7c ] corresponds to [ Fig. 7b ] for a second axis of rotation; [ Fig. 7d ] corresponds to [ Fig. 7b ] for a third axis of rotation; [ Fig. 8a ] shows deformations of a second gyrometer also in accordance with the invention, which are generated in a first pilot mode; [ Fig. 8b ] corresponds to [ Fig. 8a ] to show deformations of a first detector mode of the second gyrometer, which are generated by a rotation about a first axis from the first pilot mode; [ Fig. 8c ] shows further deformations of the second gyrometer, which are generated in a second pilot mode; [ Fig. 8d ] corresponds to [ Fig. 8b ], to show deformations of a second detector mode of the second gyrometer, which are generated by rotation about a second axis from the second pilot mode; [ Fig. 9a ] is a perspective view of the second gyrometer, showing electrodes thereof; [ Fig. 9b ] is a first sectional view of the second gyrometer, corresponding to [ Fig. 9a ] ; [ Fig. 9c ] is a second sectional view of the second gyrometer, also corresponding to [ Fig. 9a ] ; [ Fig. 10a ] is a plan view of a first force sensor which is in accordance with the invention; [ Fig. 10b ] corresponds to [ Fig. 10a ] by showing deformations associated with a useful vibration mode of the first force sensor; [ Fig. 10c ] corresponds to [ Fig. 10a ] showing a static deformation of the first force sensor when subjected to an axial tensile force; [ Fig. 11a ] corresponds to [ Fig. 10a ] for a second force sensor which is also in accordance with the invention; [ Fig. 11b ] corresponds to [ Fig. 10b ] for the second force sensor; and [ Fig. 11c ] corresponds to [ Fig. 10c ] for the second force sensor. Description détaillée de l'invention

[0031] For the sake of clarity, the dimensions of the elements shown in these figures do not correspond to real dimensions or to real dimensional ratios. In particular, all resonator deformations shown are exaggeratedly enlarged to make them visible. Furthermore, identical references in different figures designate identical elements or measurements, or which have identical functions.

[0032] A first resonator according to the invention is now described with reference to [ Fig. 4a ]-[ Fig. 4d ]. This first resonator comprises a support part, or fixed part designated by the reference Pf, a vibrating portion, and a foot Pd which connects the vibrating portion to the fixed part Pf. Preferably, the fixed part Pf, the vibrating portion and the foot Pd are formed simultaneously in a wafer with parallel faces by chemical etching, so that these three resonator parts are continuous in material. The wafer used may have a thickness of between a few micrometers and a few millimeters, when this thickness is measured perpendicular to its faces. The vibrating portion of the resonator of [ Fig. 4a ]-[ Fig. 4d ] comprises two extensions P 1 and P 2 which extend from the foot Pd and which form between them a non-zero angle α. The two extensions P 1 and P 2 extend symmetrically on either side of a median axis which coincides with a longitudinal direction of the foot Pd. This median axis corresponds to the intersection between a first plane of symmetry which is parallel to the faces of the plate and located at mid-thickness thereof, and a second plane of symmetry which is orthogonal to the faces of the plate and for which the two extensions P 1 and P 2 correspond by mirror symmetry. In the remainder of this description, and by analogy with a tuning fork resonator as described in US 3,683,213, the two extensions P 1 and P 2 are also called beams P 1 and P 2 . According to the invention, a longitudinal slot is provided on each beam P 1 , P 2 , and designated by the reference FL 1 , FL 2 respectively.These two longitudinal slots FL 1 and FL 2 meet at the median axis of the resonator. Each beam P i , the index i being equal to 1 or 2, is thus made up of two blades L iext and L iint . In the general part of the present description, the blade L 1ext (respectively L 2ext ) has been called the primary segment of the extension P 1 (resp. P 2 ), and the blade L 1int (respectively L 2int ) has been called the secondary segment of the extension P 1 (resp. P 2 ). Thus, the two blades L 1ext and L 2ext are connected to the foot Pd, and extend to respective distal ends of the extensions P 1 and P 2 , where they are connected one-by-one to the two blades L 1int and L 2int . Thus, each extension P 1 , P 2 forms a meander between the median axis and its distal end. In addition, the blades L 1int and L 2int are connected to each other at the level of the median axis, by respective proximal ends of these two blades L 1int and L 2int .The two longitudinal slots FL 1 and FL 2 of the beams P 1 and P 2 , respectively, also meet at the median axis, so that the junction of the respective proximal ends of the two blades L 1int and L 2int is separated from the blades L 1ext and L 2ext and the foot Pd. As shown in [. Fig. 4b ], when, during a vibration of the resonator, the distal ends of the beams P 1 and P 2 deviate symmetrically from the median axis in opposite directions, the plates L 1ext and L 2ext have respective momentums, MV 1 and MV 2 , which are oriented towards the same side of the resonator as the foot Pd, obliquely but symmetrically, and the common junction of the plates L 1int and L 2int has a momentum MV 12 which is parallel to the median axis while being oriented opposite to the foot Pd. As a result, the plates L 1int and L 2int have respective momentums which are oriented towards the side of the resonator which is opposite to the foot Pd, obliquely but symmetrically. Then, according to an optimization proposed by the invention, a mass distribution in the vibrating portion between all the blades L 1ext , L 2ext , L 1int and L 2int can be such that a displacement of the foot Pd which results from these quantities of movement is zero or almost zero.Due to such absence of displacement of the foot Pd, the transmission of vibration energy from the vibrating portion to the supporting part Pf is zero or very low, so that the quality factor of the resonator can be high. The optimized mass distribution between the four blades of the vibrating part is still symmetrical with respect to the center axis, and can be obtained by assigning a common thickness e ext to the two blades L 1ext and L 2ext which is different from that of the two blades L 1int and L 2int , denoted e int . When such an optimization is applied, the resonator is said to be balanced. The blade thicknesses e ext and e int are measured parallel to the faces of the plate.

[0033] According to two improvements of the invention which are shown together in [ Fig. 5a ] but which can be used independently of each other, the vibrating part of the resonator can be completed by two inertial masses MI 1 and MI 2 for the first improvement, and by a peduncle Pc for the second improvement. Preferably, the two inertial masses MI 1 and MI 2 are located at the distal ends of the two beams P 1 and P 2 , and are identical. They can each be formed by a widening of the corresponding beam P 1 , P 2 at its distal end. The peduncle Pc can be formed by an additional blade which extends from the junction of the proximal ends of the blades L 1int and L 2int , parallel to the median axis and superimposed on it, in a direction which is opposite to the foot Pd. Advantageously, the peduncle Pc is also symmetrical with respect to the median axis.The addition of the two inertial masses MI 1 and MI 2 , and / or that of the peduncle Pc, to the vibrating portion of the resonator makes it possible to obtain the balancing of the latter with additional degrees of freedom. [. Fig. 5b ] shows the displacements of the inertial masses MI 1 and MI 2 as well as that of the peduncle Pc at the same instant during the vibration of the resonator. The two inertial masses MI 1 and MI 2 then have momentum components along the median axis which are opposite to that of the peduncle Pc. These momentum components of the inertial masses MI 1 and MI 2 and of the peduncle Pc combine with those of the four blades L 1ext , L 2ext , L 1int and L 2int to produce the displacement of the foot Pd, which is zero or substantially zero when applying the invention.

[0034] It should be noted that such resonator balancing is naturally obtained for a parallel beam tuning fork as known from the prior art and shown in [ Fig. 3a ], since the two beams P 1 and P 2 are identical. The momentums of the two beams P 1 and P 2 are still referenced MV 1 and MV 2 , respectively. Such a resonator conforming to [ Fig. 3a ] does not cause its foot Pd to move parallel to its median axis X during its vibrations, because the momentums MV 1 and MV 2 are perpendicular to this median axis. Moreover, for the vibration mode where the two beams P 1 and P 2 move in phase opposition, the momentums MV 1 and MV 2 of the two beams balance if the two beams P 1 and P 2 are identical. The tuning fork resonator is then balanced. There is therefore no transmission of vibrational energy by beams P 1 and P 2 to the foot Pd, neglecting the deformations of this foot at the level of the embedding of the two beams P 1 and P 2 , which are produced by the bending moments Mf 1 and Mf 2 and the shear forces T 1 and T 2 , which is all the more true as the separation gap between the two beams P 1 and P 2 is narrow.However, as mentioned above, such a resonator with parallel and symmetrical beams cannot be made solely by chemical etching of a wafer of trigonal crystalline material of class 32, because of etching facets that appear and break the shape symmetry between the two beams P 1 and P 2 . To obtain two beams that have symmetrical shapes, it is possible to make the resonator with its two beams P 1 and P 2 that are parallel to the Yc+ and Yc- axes of the trigonal crystalline material of class 32, and with the median axis of the resonator that is parallel to the crystallographic axis Xc. But then the two beams P 1 and P 2 of the tuning fork are no longer parallel, and it becomes impossible to balance the resonator for this reason. Thanks to the use of the longitudinal slots FL 1 and FL 2 according to the invention, in the resonator of [. Fig. 4a ]-[ Fig. 4d ], the balancing of the resonator is again possible although its beams P 1 and P 2 are not parallel to each other.

[0035] The inventors indicate that it is however possible to balance the resonator of [ Fig. 3b ] with non-parallel beams by symmetrizing its vibrating portion with respect to the YZ plane. The vibrating portion thus comprises four beams P 1 , P 2 , P 3 and P 4 which can have symmetrical shapes such as resulting from the chemical etching of a class 32 trigonal crystalline material. The Pd foot of the resonator is then located at the junction of the four beams. In this case, the resonator is balanced for a vibration mode in which the two tuning forks vibrate in phase. However, the double tuning fork resonator configuration which is thus obtained, as represented in [ Fig. 3c ], is more bulky and may be poorly suited to applications where significant miniaturization is required. For such applications, the [ Fig. 4a ]-[ Fig. 4d ] Or [ Fig. 5a ]-[ Fig. 5b ] may be preferred.

[0036] For the resonator of [ Fig. 4a ]-[ Fig. 4d ] Or [ Fig. 5a ]-[ Fig. 5b ], the angle α between the two beams P 1 and P 2 is equal to 60°. In this way, it is possible to obtain symmetrical realizations by chemical etching of a wafer with parallel faces which is made of a trigonal crystalline material of class 32, by orienting the beams P 1 and P 2 longitudinally parallel to the crystallographic axes Yc+ and Yc-, and the median axis parallel to the crystallographic axis Xc, the faces of the wafer being perpendicular to the Z axis. For example, the material of the wafer can be monocrystalline α quartz, which is piezoelectric. In this case, the resonator can be provided with two electrodes as shown in [ Fig. 4c] et [Fig. 4d ]. As is known, these electrodes can serve both as means of exciting the symmetrical vibration mode, and as means of detecting the vibration amplitude in this same mode. The references in these two figures have the meanings mentioned below: pour la première électrode , which can be connected to an electrical ground: PC 1 segment of the first electrode which is carried by the support part Pf of the resonator el 1-PC1 segment of the first electrode which is carried by the foot Pd of the resonator el 1 segment of the first electrode which is carried by the blade L 1ext along an external edge thereof, on a first of the two faces of the plate el 3 segment of the first electrode which is carried by the blade L 1ext along an internal edge thereof, on the first face of the plate el 4 segment of the first electrode which is carried by the blade L 1int along an internal edge thereof, on the first face of the plate el 6 segment of the first electrode which is carried by the blade L 1int along an external edge thereof, on the first face of the plate el 7 and el 9 correspond to el 6 and el 4 , respectively, for blade L 2int el 10 and el 12 correspond to el 3 and el 1 , respectively,for blade L 2ext el 1-6 electrical connection segment between segments el 1 and el 6 at the distal end of beam P 1 , on the first face of plate el 3-4 electrical connection segment between segments el 3 and el 4 at the distal end of beam P 1 , on the first face of plate el 7-9 electrical connection segment between segments el 7 and el 9 at the distal end of beam P 2 , on the first face of plate el 10-12 electrical connection segment between segments el 10 and el 12 at the distal end of beam P 2 and on the first face of plate. The first electrode segments el 6 and el 7 are connected to each other at the median axis, as are the segments el 4 and el 9 , and as are the segments el 3 and el 10 . , pour la seconde électrode, which can be connected to a source of alternating electric potential V: PC 2 and el 2-PC2 correspond to PC 1 and el 1-PC1, respectively, and for the second electrode el 2 segment of the second electrode which is carried by the blade L 1ext in a central part thereof, on the first face of the plate els, els and el 11 correspond to el 2 for the blades L 1int, L 2int and L 2ext, respectively el 2-5 electrical connection segment between the segments el 2 and el 5 at the distal end of the beam P 1, on the first face of the plate. The second electrode segments el 5 and el 8 are connected to each other at the median axis, as are the segments el 2 and el 11.The electrode segments el 10n, for the integer index n varying from 1 to 12, correspond respectively to the segments el n for the second face of the wafer, with electrical connection segments which are analogous to those described for the first face of the wafer. Finally, the segments of the same of the two electrodes which are located on one and the other of the two faces of the wafer are electrically connected to each other, either by an electrical connection carried by the resonator, or by an external electrical connection.

[0037] Each electrode segment may consist of a strip of conductive material such as gold (Au), for example deposited using a thin-film formation technique, and have a width equal to 200 µm (micrometer). In accordance with the enumeration just provided, three parallel strips are arranged on each blade face, making a total of twelve conductive strips per face of the wafer, el 1 to el 12 on the first face and el 101 to el 112 on the second face. As already explained with reference to the [ Fig. 1a ], the three conductive strips on each blade face allow excitation and detection that are effective for bending vibrations of the blade parallel to the Xc-Yc plane, when this blade extends longitudinally along the crystallographic axis Yc+ or Yc-. For increased efficiency of the piezoelectric coupling, it is advantageous for the strips of the first electrode to be relatively thin, with strip widths that are between 1 / 10 and 1 / 5 of the thickness e ext or eint of the blades L 1ext , L 2ext , L 1int and L 2int . For the strips of the second electrode, their widths can be between two and five times those of the strips of the first electrode.

[0038] Such a piezoelectric vibration excitation and detection electrode scheme is suitable for the bending vibration mode where the two beams P 1 and P 2 move in phase opposition, as shown in [ Fig. 4b ]. However, other electrode configurations are alternatively possible, for example by depositing strips of conductive material on the sides of the blades which are perpendicular to the faces of the wafer. In this case, the strips el 1 and el 101 are replaced by a single strip on the side of the blade L 1ext , and similarly for the pairs of strips of the first electrode which are carried separately by the other blades L 1int , L 2int and L 2ext . Each blade side then carries two strips which are each close to an edge of the side opposite to that of the other strip, with one of the two strips belonging to the first electrode, and the other strip belonging to the second electrode. This other electrode configuration is more efficient than that of [ Fig. 4c ]-[ Fig. 4d ] for piezoelectric coupling, but at the cost of greater complexity of production.

[0039] The resonator can thus be associated with an oscillating electronic loop, which is connected at the input to the segments PC 1 of the first electrode on the support part Pf of the resonator, and at the output to the segments PC 2 of the second electrode also on the support part Pf. The vibration mode for which the two beams P 1 and P 2 move in phase opposition is thus excited by the alternating voltage V which is applied by the oscillating electronic loop between the two electrodes, and the vibration amplitude of the resonator for this same mode is detected by the electric current which is generated by the vibrations of the resonator in the two electrodes. For this, a current detection circuit can be used in the oscillating electronic loop, which advantageously has a high input impedance.

[0040] The inventors now provide some rules which make it possible to balance according to the invention a resonator conforming to [ Fig. 4a ]-[ Fig. 4d ], i.e. without the inertial masses MI 1 , MI 2 nor the peduncle Pc. The frequency F of the resonator for the considered bending vibration mode, where the two beams P 1 and P 2 move symmetrically in phase opposition, can be approximated using the following equation (equation 1): F en Hertz ≅ 0.58 ⋅ e int L int 2 ⋅ e ext L ext 2 e int 2 L int 4 + e ext 2 L ext 4 ⋅ e int ⋅ e int + F l e ext + F l L int ⋅ L ext ⋅ E ρ with the following meanings, already given for some of them: e int : common thickness of the blades L 1int and L 2int , measured parallel to the faces of the wafer and expressed in meters e ext : common thickness of the blades L 1ext and L 2ext , measured parallel to the faces of the wafer and expressed in meters L int : common length of the blades L 1int and L 2int , expressed in meters L ext : common length of the blades L 1ext and L 2ext , expressed in meters F l : common width of the longitudinal slots FL 1 and FL 2 in the extensions P 1 and P 2 , measured parallel to the faces of the wafer and expressed in meters E : Young's modulus of the wafer material, expressed in newtons per square meter (N / m 2 < ) ρ : density of the wafer material, expressed in kilograms per cubic meter (kg / m 3 < ).

[0041] To allow compensation at the foot Pd of the components of quantities of movement parallel to the axis Xc, it is also necessary that the dimensions e int , e ext , L int and L ext verify the following condition (equation 2): e ext e int 0 , 5 ⋅ L ext e ext 3 − L int e int 3 L ext e ext 3 + L int e int 3 ≅ 0 , 64 Now this condition means that the slenderness L ext / e ext of each blade L 1ext , L 2ext is greater than the slenderness L int / e int of each blade L 1int , L 2int . Equation 2 can also be written in the following form (equation 3): L ext L int = e ext e int ⋅ 1 + k 1 − k 1 3 avec k = 0 , 64 ⋅ e int e ext 1 2 The positivity of 1-k allows us to give a first bound for the quotient e ext / e int: this quotient is greater than 0.4. Furthermore, by construction, the following equation links the blade lengths L ext and L int , via the angle α which separates the two beams P 1 and P 2 (equation 4): L ext = L int + 2 ⋅ F l + e int + e ext 2 ⋅ tan α 2 The last three equations, with the five unknowns e ext , e int , L ext , L int and F l , allow the person skilled in the art to choose the dimensions of the resonator according to the intended applications and technological constraints, in particular according to the space available for the resonator in each application.

[0042] For example, with a crystal plate of the trigonal system of symmetry class 32, such as α quartz which is piezoelectric, and for an angle α of 60° between the two beams P 1 and P 2 , each oriented parallel to a crystallographic axis Yc, one parallel to Yc+ and the other to Yc-, to guarantee the symmetry of the resonator as obtained by chemical etching as already explained, it is possible to size a balanced resonator with a slenderness P int =L int / e int common to the plates L 1int and L 2int , which is between 3 and 10, and another slenderness P ext =L ext / e ext common to the plates L 1ext and L 2ext , which is between 8 and 30, and with a quotient e int / e ext which is between 1 and 5. For example, L int ~2.5 mm (millimeter), e int ~0.24 mm, L ext ~3.3 mm, e ext ~0.15 mm and F l ~0.27 mm, producing a vibration frequency F of the resonator which is equal to 32 kHz (kilohertz).This same value of 32 kHz for the frequency F can also be obtained with L int ~4.95 mm, e int ~1.5 mm, L ext ~8.9 mm, e ext ~1.7 mm and F l ~0.7 mm, which shows the extent of the sizing possibilities to obtain a balanced resonator using the invention.

[0043] For resonators intended to vibrate in bending, the intrinsic quality coefficient of the resonator is limited by the thermoelastic losses that are generated by heat exchange between compressed and stretched fibers of each blade during vibration, as was theorized in the article by C. Zener, entitled "Internal friction in solids", Physical Review 52, ​​August 1937, pp.230-235. In the case of quartz and for a simple beam in bending vibration at a frequency that is between a few kilohertz and a few hundred kilohertz, the thermoelastic quality coefficient is proportional to the frequency F of the resonator multiplied by the vibrating thickness e squared: Q thermoelastic (quartz) ∝ Fe 2< .In the case of silicon and for the same frequency interval, this thermoelastic coefficient is proportional to the frequency F of the resonator divided by the vibrating thickness e squared: Q thermoelastic (silicon) ∝ F / e 2< , which leads to resonator dimensions which are very different between these two crystals. Thus, in the case of quartz and when stability performances of the resonator frequency are sought, dimensions which correspond to large values ​​for the thicknesses e int and e ext are favored, and vice versa for silicon.

[0044] Compared to a resonator configuration conforming to [ Fig. 4a ], the addition of the peduncle Pc modifies the quantity of movement which is generated along the Xc axis by the vibration: a component of quantity of movement of the peduncle Pc is added to those of the blades L 1int and L 2int . It thus makes it possible to increase the sizing possibilities which produce a balancing of the resonator. In particular, the addition of the peduncle Pc makes it possible to increase the thickness e ext of the blades L 1ext and L 2ext compared to the configuration without peduncle of [ Fig. 4a ].

[0045] Again with respect to a resonator configuration conforming to [ Fig. 4a ], the addition of the inertial masses MI 1 and MI 2 to the distal ends of the beams P 1 and P 2 also makes it possible to modify the distribution of momentum between all parts of the vibrating portion. In particular, the addition of the inertial masses MI 1 and MI 2 makes it possible to increase the thickness e int of the blades L 1int and L 2int to an equal value of the length L int of these.

[0046] The resonator of [ Fig. 6a] ou [Fig. 6c ] corresponds to that of [ Fig. 5a ] but with the angle α which is equal to 180° instead of 60°, without peduncle for [ Fig. 6a ] and with peduncle Pc for [ Fig. 6c ]. The blade lengths L ext and L int then become equal, and the condition of equation 3 for resonator balancing, provided previously for a resonator without the peduncle Pc nor the inertial masses MI 1 and MI 2 , can no longer be satisfied. The inertial masses MI 1 and MI 2 are necessary when the angle α is equal to 180°, to obtain the compensation of the momentum quantities. The vibration mode which is represented on [ Fig. 6b ] when the resonator is without a peduncle, or on [ Fig. 6d ] when the resonator includes the peduncle Pc, corresponds mainly to a bending vibration of the continuous blade which is the union of the two previous blades L 1int and L 2int , with a total length equal to the sum of their individual lengths, and with still the thickness e int . The frequency F of the resonator for this mode of vibration can be approximated by the following equation (equation 5): F en Hertz ≅ e int L int 2 ⋅ L int ⋅ e int L c ⋅ e c + L int ⋅ e int 3 4 ⋅ E ρ with : L int: total length of the blade measured between the two inertial masses MI 1 and MI 2 , and expressed in meters e int: width of the blade which is opposite the foot Pd, measured parallel to the faces of the plate and expressed in meters L c: length of the peduncle Pc, measured parallel to the faces of the plate and expressed in meters ec: width of the peduncle Pc, measured parallel to the faces of the plate and expressed in meters. E: Young's modulus of the plate material, expressed in newtons per square meter (N / m 2< ) ρ: density of the plate material, expressed in kilograms per cubic meter (kg / m 3< ).

[0047] To allow the compensation of the quantities of movement along the Xc axis, it is also necessary that the dimensions e int , e ext , L int , e Mi , L Mi , L c and ec respect the following double inequality (equation 6): 1 ≤ J L int ⋅ e int + L c ⋅ e c ⋅ e int e ext ⋅ e int + e ext L int ≤ 3 , 5 with the following additional meanings: e ext: width of the blade which is connected to the foot Pd, measured parallel to the faces of the plate and expressed in meters e Mi: common width of the inertial masses MI 1 and MI 2 , measured parallel to the blades and expressed in meters L Mi: common length of the inertial masses MI 1 and MI 2 , measured parallel to the axis Xc and expressed in meters J: moment of inertia per unit of surface mass of the inertial masses MI 1 and MI 2 , which is equal to (equation 7): J = L Mi ⋅ e Mi ⋅ L Mi 2 + e Mi 2 The double inequality of equation 6 allows us to size the resonators of [ Fig. 6a ]-[ Fig. 6d ] so that they are balanced, from certain values ​​which are initially chosen according to the characteristics sought for these resonators.

[0048] Eventually, the dimensioning of each of the resonators that have been presented above, using the rules provided previously, could be continued using numerical simulations such as finite element calculations, to achieve more precise balancing of these resonators.

[0049] A resonator as described above can be used to form a gyrometer with one or more sensitive axes. A sensitive axis of the gyrometer is a rotation axis for which the gyrometer can measure rotational speed around this axis. To obtain a gyrometer with three sensitive axes, allowing rotational speed components to be measured respectively along the X, Y and Z axes, a resonator for which the angle α is different from 0° and 180° is necessary. Such a resonator for which the angle α is equal to 60° is preferred. The Coriolis acceleration produces, during rotation of the resonator, an additional displacement of each blade of the resonator which is perpendicular to the displacement of this blade for the pilot mode. Fig. 7a ] recalls the simultaneous displacements of the beams P 1 and P 2 , as well as of the peduncle Pc, for a resonator according to the invention with α equal to 60°, and when the vibration mode which is excited by the electrodes, that is to say the pilot mode, is that where the two beams P 1 and P 2 move in phase opposition parallel to the faces of the plate, like a tuning fork. MV 1 , MV 2 and MV c designate the respective quantities of movement of the beams P 1 , P 2 and of the peduncle Pc. [ Fig. 7b ] shows the corresponding Coriolis accelerations, denoted Γ C , which are produced by a rotation around the X axis, with a rotation speed Ω x , [ Fig. 7c ] shows those produced by a rotation around the Y axis, with a rotation speed Ω y , and [ Fig. 7d ] shows those produced by a rotation about the Z axis, with a rotation speed Ω z . These Coriolis accelerations are perpendicular to the wafer for rotations about the X and Y axes, with the dot symbol surrounded by a circle to represent a Coriolis acceleration that is directed towards the reader, and a cross surrounded by a circle to represent a Coriolis acceleration that is directed in the direction of view of the reader. However, the inertial forces resulting from these Coriolis accelerations are not balanced at the Pd foot, so it is preferable to provide additional means to limit the vibration energy losses that occur through the Pd foot of the resonator. For example, a decoupling structure as described in US 6,414,416 B1 in the name of the applicant, could be used for a gyrometer with a single sensitive axis which would be the X axis (cf. [ Fig. 7b]), since this decoupling structure is effective in reducing or avoiding a transmission of torsional movements to the fixing part of the resonator by its foot Pd. For a gyrometer with a single sensitive axis which would be the Y axis (cf. [ Fig. 7c ]), the vibration mode which is coupled to the pilot mode of [ Fig. 7a ] by the rotation speed Ω y is a mode where both beams P 1 and P 2 undergo out-of-plane phase bending, and the peduncle Pc undergoes out-of-plane bending which is in phase opposition with respect to beams P 1 and P 2 . But the resulting forces do not balance at the foot Pd of the resonator, and a residual moment is transmitted to the fixing part of the resonator by its foot Pd. The forces which are generated during a rotation around the Z axis (cf. [ Fig. 7d ]) from the pilot mode of [ Fig. 7a ] are parallel to the plate, but do not balance each other either.

[0050] To balance the forces and moments which are transmitted to the fixing part Pf of the resonator, a new gyrometer is proposed by the invention, which comprises two vibrating portions each similar to that of [ Fig. 7a ], oriented opposite each other and with a common foot Pd. The two vibrating portions are made from the same wafer, so that they are continuous in material through the foot Pd. Such a gyrometer, which is shown in [ Fig. 8a ]-[ Fig. 8d ] is effective for measuring rotations around the X axis, or around the Y axis. Two excitation vibration modes are possible as pilot modes, each of which preserves the balancing provided by the double-resonator structure: an out-of-phase mode, for which the two beams P 1 and P 2 of one of the vibrating portions move away from each other and tighten in out-of-phase with respect to the beams P 3 and P 4 of the other vibrating portion, as shown in [ Fig. 8a ], and an in-phase mode, for which the two beams P 1 and P 2 of one of the vibrating portions move away from each other and tighten in phase with the beams P 3 and P 4 of the other vibrating portion, as shown in [ Fig. 8c ]. In these two figures, each inscription MV designates the quantity of movement of the beam or peduncle on which it is superimposed. Fig. 8b ] shows the balancing of the inertial forces that result from the Coriolis accelerations Γ C for the excitation vibration mode of [ Fig. 8a ] used as pilot mode, and [ Fig. 8d ] for the excitation vibration mode of [ Fig. 8c ] used as a pilot mode. One or the other of these two excitation modes is selected as the pilot mode by the configuration of the electrodes on the two vibrating portions. For example, in the case of the piezoelectric quartz crystal or any other piezoelectric crystal of the same symmetry class, the gyrometer may consist of two head-to-tail vibrating portions, each with two beams forming an angle of 60° between them, so that these beams are parallel to the crystallographic axes Yc+ and Yc-. [ Fig. 9a ]-[ Fig. 9c ] show a set of ribbons of conductive material which are arranged on the faces of all segments of the two vibrating portions. The two vibrating portions are designated by the letters A and B, respectively, and correspond to the sectional view of [ Fig. 9b ] for the vibrating portion A, and in the sectional view of [ Fig. 9c ] for the vibrating portion B.

[0051] For a gyrometer whose sensitive axis is the X axis, parallel to the crystallographic axis Xc, the pilot mode is the one with the two resonators vibrating in phase opposition, as illustrated by [ Fig. 8a ]. It is then possible to apply the teaching of US 2012 / 0279303 A1 in the name of the applicant to limit the capacitive couplings between the pilot mode and the detector mode. According to this teaching, the strips el 3 - A , el 103-A , el 4-A , el 104-A , el 9-A , el 109-A , el 10-A , el 110-A , el 3-B , el 108-B , el 4-B , el 104-B , el 9-B , el 110-B , el 110-B allow to excite the pilot mode by electrically connecting them to a source of alternating potential V, and by using the strips el 2-A , el 102-A , el 5-A , el 105-A , el 8-A , el 108-A , el 11-A and el 111-A to detect the amplitude of the pilot mode.So, the strips el 1-A , el 101-A , el 6-A , el 106-A , el 7-A , el 107-A , el 12-A , el 112-A , el 1-B , el 101-B , el 6-B , el 106-B , el 7-B , el 107-B , el 12-B and el 112-B can be used to detect movements that are generated by a rotation around the X axis, but by connecting the strips el 1-A , el 6-A , el 7-A , el 12-A , el 1-B , el 6-B , el 7-B and el 12-B in a part, and the strips el 101-A, el 106-A, el 107-A, el 112-A, el 101-B, el 106-B, el 107-B and el 112-B on the other hand, respectively to the input terminals of a differential amplifier forming part of an electric current detector.

[0052] For a gyrometer whose sensitive axis is the Y axis, perpendicular to the Xc axis of the crystal and in the common plane of the Xc, Yc+ and Yc- axes, the pilot mode is the one with the two resonators vibrating in phase, as illustrated by [ Fig. 8c ]. The strips el 1-A , el 101-A , el 6-A , el 106-A , el 7-A , el 107-A , el 12-A , el 112-A , el 1-B , el 101-B , el 6-B , el 106-B , el 7-B , el 107-B , el 12-B and el 112-B then allow this pilot mode to be excited by connecting them to the source of alternating potential V, and by using the strips el 2-A , el 102-A , el 5-A , el 105-A , el 8-A , el 108-A , el 11-A , el 111-A , el 2-B , el 102-B , el 5-B , el 105-B , el 8-B , el 108-B , el 11-B and el 111-B to detect the pilot mode amplitude.In this case, the strips el 3-A , el 103-A , el 4-A , el 104-A , el 9-A , el 109-A , el 10-A , el 110-A , el 3-B , el 103-B , el 4-B , el 104-B , el 9-B , el 109-B , el 10-B and el 110-B can be used to detect movements that are generated by a rotation around the Y axis, but by connecting the strips el 3-A , el 4-A , el 9-A , el 10-A , el 103-B , el 104-B , el 10-B and el 110-B on the one hand, and the strips el 103-A, el 104-A, el 109-A, el 110-A, el 3-B, el 4-B, el 9-B and el 10-B on the other hand, respectively to the input terminals of the differential amplifier which is part of the electric current detector.

[0053] Another application of resonators according to the invention is the production of a force sensor. The force sensor, as shown in [ Fig. 10a ], is based on two identical vibrating portions which are still made from the same plate, which are still oriented opposite each other but secured by their peduncles Pc. Each of the two vibrating portions is dimensioned to be balanced individually. The beams P 1 and P 2 of one of the two vibrating portions on the one hand, and those P 3 and P 4 of the other vibrating portion on the other hand, form angles of 60° between them. This association of the two vibrating portions makes it possible to obtain a double resonator whose two ends, constituted by the respective feet of the individual vibrating portions, are free or almost free of residual movement, as shown by [ Fig. 10b ], for a vibration mode where the two vibrating portions vibrate in phase opposition. When this sensor is subjected to an axial tensile force, the static deformation which is imposed on the double resonator modifies its bending inertia. [ Fig. 10c ] shows this static deformation for the axial tensile force T.

[0054] If such a force sensor is made of quartz crystal, two configurations are possible, which correspond either to an angle α which is equal to 60°, as shown in [ Fig. 10a ]-[ Fig. 10c ], or at an angle α which is equal to 180°, as shown in [ Fig. 11a ]-[ Fig. 11c ]. So, [ Fig. 11a ] shows the configuration with two vibrating portions for which the beams P 1 and P 2 on the one hand, and P 3 and P 4 on the other hand, make an angle of 180° between them. [ Fig. 11b ] shows an instantaneous deformation of the double-resonator structure of [ Fig. 11a ], for the vibration mode of interest where the two vibrating portions vibrate in phase. [ Fig. 11c] shows the static deformation of the same force sensor when subjected to the axial tensile force T. For the case where the angle α is equal to 180°, the relative variation of frequency F of the vibration mode considered, induced by the axial tensile force T, is proportional to (equation 8): ΔF F ∝ T ⋅ e int L int 3 + e ext L ext 3 Using equation 8, the person skilled in the art will be able to size the force sensor according to each application and the measurement sensitivity that is appropriate for it.

[0055] It is understood that the invention can be reproduced by modifying secondary aspects of the embodiments that have been described in detail above, while retaining at least some of the advantages cited. In particular, the material of the wafer is not necessarily a piezoelectric monocrystalline material. For example, the wafer can be made of silicon, monocrystalline or polycrystalline, or be a piezoelectric ceramic, or a combination of a metallic material and piezoelectric ceramics. The means for exciting and detecting vibrations must then be adapted according to each material. For example, the excitation can be carried out using electrostatic forces, a magnetic force, or by implementing a photo-thermal effect, etc., and the detection can be carried out by measuring a variation in capacitance of a capacitor formed between a part of the resonator which is in motion and a part which is fixed, or by using a piezo-resistive effect, or by carrying out a measurement by optical interferometry, etc. Finally, all the numerical values ​​which have been cited have been cited only for illustration purposes, and can be changed depending on the application considered.

Claims

1. A resonator comprising: - a portion of a wafer having two opposite faces which are flat and parallel, the wafer portion being intended to vibrate flexurally during use of the resonator, and referred to as the vibrating portion; and - a support part (Pf), which is external to the vibrating portion and connected thereto by an intermediate segment of the wafer referred to as a foot (Pd), said foot being integral with the vibrating portion and forming a rigid connection between the support part and said vibrating portion, the vibrating portion having a first plane of symmetry, referred to as the midplane (M), which is parallel to both faces of the wafer and equidistant from said two faces, and a second plane of symmetry, referred to as the plane of symmetry orthogonal to the wafer (P), which is perpendicular to the midplane and which passes longitudinally through the connection formed by the foot between the support part (Pf) and the vibrating portion, an intersection between the midplane (M) and the plane of symmetry orthogonal to the wafer (P) constituting a center axis of the vibrating portion, the vibrating portion comprising two extensions (P1, P2) which are each intended to vibrate flexurally, said two extensions extending symmetrically from the foot (Pd) on each side of the plane of symmetry orthogonal to the wafer (P), the resonator being characterized in that each extension (P1, P2) is provided with a longitudinal slot (FL1, FL2) which passes through the vibrating portion perpendicularly to the midplane (M), from the plane of symmetry orthogonal to the wafer (P) towards a distal end of said extension but without reaching said distal end, so that each extension is meander shaped, the respective slots (FL1, FL2) of the two extensions (P1, P2) being symmetrical relative to the plane of symmetry orthogonal to the wafer (P), and meeting at said plane of symmetry orthogonal to the wafer, so that the vibrating portion comprises two primary segments (L1ext, L2ext) which each connect the foot (Pd) to the distal end of one of the extensions, and two secondary segments (L1int, L2int) which are interconnected at the plane of symmetry orthogonal to the wafer by respective proximal ends of said secondary segments, and which each extend to the distal end of one of the extensions so as to connect to one of the primary segments at said distal end, such that for a mode of vibration of the vibrating portion which comprises only movements parallel to the midplane (M), and which is symmetrical relative to the plane of symmetry orthogonal to the wafer (P), both primary segments (L1ext, L2ext) have instantaneous velocity components, parallel to the center axis, which at each instant during vibration, are in the opposite direction to that of instantaneous velocity components of the secondary segments (L1int, L2int), also parallel to the center axis.

2. The resonator according to claim 1, wherein the vibrating portion has a distribution of mass such that the mode of vibration, which only comprises movements parallel to the midplane (M) and which is symmetrical relative to the plane of symmetry orthogonal to the wafer (P), does not cause movement of the foot (Pd) parallel to the center axis.

3. The resonator according to claim 1 or 2, wherein a material of the wafer is monocrystalline and of trigonal class and piezoelectric, and wherein: the center axis of the vibrating portion is parallel to an axis Xc of said material, and both primary segments (L1ext, L2ext) as well as both secondary segments (L1int, L2int) of the vibrating portion are parallel to axes Yc of said material.

4. The resonator according to claim 3, wherein both extensions (P1, P2of the vibrating portion form an angle (α) between them which is equal to 60° or 180°.

5. The resonator according to claim 3 or 4, further comprising: - excitation means, adapted for generating flexural deformations of the vibrating portion, said excitation means comprising first and second electrodes which are electrically insulated from each other, said first electrode comprising, on each face of the wafer and for each primary (L1ext, L2ext) or secondary (L1int, L2int) segment, a strip of electrically conducting material which is arranged longitudinally on said segment, centrally within a width of said segment, and the second electrode comprising, also on each face of the wafer and for each primary or secondary segment, two strips on said segment which are arranged on two opposite sides of the strip of the first electrode; and - detection means, adapted for measuring an amplitude of flexural deformations of the vibrating portion which are generated by the excitation means during use of the resonator, said detection means comprising a circuit for detecting an electrical current which appears in the first and second electrodes.

6. The resonator according to any one of the preceding claims, wherein each extension (P1, P2) comprises, at its distal end and parallel to the midplane (M), a widening relative to the outer longitudinal edges of the primary (L1ext, L2ext) and secondary (L1int, L2int) segments of said extension.

7. The resonator according to any one of the preceding claims, further comprising an additional portion of the wafer, in the form of a segment and referred to as a stem (Pc), which extends from the interconnected proximal ends of the secondary segments (L1int, L2int), parallel to the center axis and in a direction away from the foot (Pd).

8. The resonator according to claim 7, comprising two vibrating portions formed in the same wafer, provided with respective stems (Pd), said two vibrating portions being interconnected by said stems, and oriented opposite to each other so that the respective center axes of said two vibrating portions are superimposed.

9. The resonator according to any one of claims 1 to 7, comprising two vibrating portions formed in the same wafer, both vibrating portions being interconnected by the respective feet (Pd) of said two vibrating portions, and oriented opposite to each other so that the respective center axes of said two vibrating portions are superimposed.

10. A force sensor, comprising a resonator according to claim 8, and adapted for measuring a tensile force which is applied between the respective feet (Pd) of both vibrating portions and which is parallel to the center axes of said two vibrating portions.

11. A rate gyro, comprising at least one resonator according to any one of claims 1 to 9.